A345901 a(n) is the largest k such that the tribonacci word A080843 contains a block of length k*n that is an abelian k-th power.

2, 2, 2, 3, 2, 4, 5, 2, 2, 2, 4, 2, 8, 2, 2, 2, 4, 3, 2, 6, 2, 2, 2, 8, 2, 4, 3, 2, 2, 3, 6, 2, 3, 2, 2, 2, 10, 3, 2, 3, 3, 3, 3, 13, 2, 2, 2, 4, 2, 5, 4, 2, 2, 2, 5, 2, 6, 2, 2, 2, 6, 3, 3, 4, 2, 2, 2, 12, 2, 3, 2, 2, 2, 5, 5, 2, 3, 2, 3, 2, 21, 2, 2, 2, 4, 3

Offset: 1

Author

Jeffrey Shallit, Jun 29 2021

Keywords

• nonn

Comments

An abelian k-th power consists of k blocks x_1 x_2 ... x_k such that each x_i is a permutation of x_1. For example, the English word "deeded" is an abelian 3rd power.

Examples

			For n=4, A080843 contains the block 2010.0102.0102, which is an abelian 3rd power. But no blocks of size 16 in A080843 are abelian 4th powers.
		

Crossrefs

Cf. A080843.